Unformatted text preview: G . Prove that G is connected if there is a value of k such that A k has no zero entries; show additionally that the converse is not necessarily true. 5. (5 point bonus) Prove that every tree T has at least Δ( T ) leaves. The origins of graph theory are humble, even frivolous. Whereas many branches of mathematics were motivated by fundamental problems of calculation, motion, and measurement, the problems which led to the development of graph theory were often little more than puzzles, designed to test the ingenuity rather than to stimulate the imagination. —Biggs, Lloyd, and Wilson, Graph Theory: 1736–1936 Page 1 of 1 Due January 21, 2010...
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 Spring '09
 WILDSTROM
 Math, Graph Theory, graph G. Prove

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